Bisecting a Segment The midpoint of a segment is the point that divides or bisects the segment into two congruent segments A segment bisector is a segment ray line or plane that intersects a segment ID: 641666
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Slide1
Geometry
1.5 Segment and Angle BisectorsSlide2
Bisecting a Segment
The
midpoint
of a segment is the point that divides, or bisects, the segment into two congruent segments.A segment bisector is a segment, ray, line, or plane that intersects a segment at its midpointSlide3
Finding the Midpoint
If you know the coordinates of the endpoints of a segment, you can calculate the coordinates of the midpoint. You simply take the mean, or average, of the x-coordinates and of the y-coordinates. This method is summarized as the
Midpoint FormulaSlide4
Midpoint FormulaSlide5
Find the Midpoint
Graph the points A(-2, 3) and B(5, -2)
Use the Midpoint Formula to find the coordinates of the midpoint of segment AB.Slide6
Find the Midpoint
Graph the points D(3,
5
) and E(-4, 0)Use the Midpoint Formula to find the coordinates of the midpoint of segment DE.Slide7
Bisecting an Angle
An
angle bisector
is a ray that divides an angle into two adjacent angles that are congruent.Slide8
Example 1
The ray FH bisects the angle EFG. Given that the measure of angle EFG = 120 degrees, what are the measures of angle EFH and angle HFG?Slide9
Example 2
Angle CBA is bisected by ray BD. The measure of angle DBA is 65 degrees. Find the measure of angle CBA.Slide10
Example 3
In the diagram, ray RQ bisects angle PRS. The measures of the two congruent angles are (x+40) degrees and (3x – 20) degrees. Solve for x.
(x + 40)
(3x – 20)